Reliability Ratio-Based Serial Algorithm of LDPC Decoder for Turbo Equalization Schemes

Serial decoding algorithms of low-density parity-check (LDPC) code converge efficiently with low errors. Previously, a serial decoding algorithm, named a shuffled belief-propagation (SBP), was applied in turbo equalization of bit-patterned magnetic recording (BPMR) systems. With the SBP algorithm, an LDPC decoder converged twice as fast as one using conventional BP algorithms. We further improved the convergence speed of SBP by updating the messages in an adaptive order, which played a flexible role throughout decoding. We proposed two adaptive-serial algorithms for LDPC codes in turbo equalization. One updated the messages using the extrinsic loglikelihood ratio (LLR) and the result of the parity-check equation checking. The second contained an additional rule that tracked the LLR sign changes in each iteration. Both algorithms converged faster and with lower bit error rates (BERs) than the SBP and previous adaptive-serial algorithms in a BPMR system with media noise.